Apparatus and method for measuring thickness of thin semiconductor multi-layer film

ABSTRACT

An interference waveform dispersion spectrum of light reflected from a multi-layer film is compared to a waveform obtained by numerical calculation using an optical characteristic matrix. Respective layer thickness values obtained from the calculated analysis of the Spatial interference waveform are subjected to waveform fitting with actually measured values. The theoretical interference spectrum is recalculated while changing approximate values of the layer thicknesses until a match is obtained to obtain precise respective layer thicknesses. The thicknesses of respective layers of a thin multi-layer film of submicron thicknesses can be non-destructively measured exactly and stably without direct contact.

This disclosure is a division of patent application Ser. No. 08/262,840,filed Jun. 21, 1994.

FIELD OF THE INVENTION

The present invention relates to an apparatus and a method for measuringthe thickness of a thin semiconductor multi-layer film and, moreparticularly, to an improvement in an apparatus for non-destructivelymeasuring, without direct contact, the thicknesses of respective layersof a thin multi-layer film of epitaxially grown crystallinesemiconductor layers.

BACKGROUND OF THE INVENTION

Recently, thin film techniques have been advancing. For example,semiconductor devices having various pattern structures with submicronfeatures have been developed, such as semiconductor lasers, GaAs HEMTs(high electron mobility transistors), and HBTs (heterojunction bipolartransistors). To produce these semiconductor devices with a high degreeof repeatability, particularly in compound semiconductor devices, it isimportant to control the thicknesses of epitaxially grown thincrystalline films.

Conventionally, thicknesses of thin films are measured in a cleavedcross-section of a sample with an SEM (scanning electron microscope).However, this method is destructive and requires etching of a sampleand, therefore, cannot be used in a manufacturing line.

A non-destructive interference method of measuring layer thickness hasrecently been used. This method employs Fourier Transformation InfraredSpectroscopy (hereinafter referred to as FTIR) apparatus having aFourier transformation processing function and a light dispersingspectroscopy apparatus. This method comprises irradiating a sample withinfrared light having a relatively wide wavenumber range from farinfrared to near infrared, having a spectrum wavenumber modulation bandof 0 to 32000 cm⁻¹ and Fourier transformation of the interferencespectrum to produce a space interference waveform (hereinafter referredto as Spatialgram), thereby evaluating the thicknesses of the layers ofthe multi-layer film.

FIG. 4(a) is a block diagram illustrating the construction of the FTIRapparatus. In FIG. 4(a), reference numeral 13 designates a Michelsoninterferometer emitting an interference light flux that is modulated intime. Numeral 26 designates a photometry system for spectrometry of thereflected light obtained by irradiating a sample with measuring lightfrom the interferometer 13. Numeral 150 designates a spectroscopyapparatus comprising the Michelson interferometer 13 and the photometrysystem 26 for continuous spectrometry of the reflected light from themulti-layer film in a range from visible light to the far infrared.Numeral 200 designates a data processing apparatus for Fouriertransformation of the electrical signal that is obtained from the lightmeasurement by the photometry system 26 of the spectroscopy apparatus150 and further analysis of the signal.

FIG. 4(b) is a flowchart schematically illustrating the data processingperformed by the FTIR apparatus. In the figure, reference numeral 200adesignates measuring the interference light intensity waveform. Numeral200b designates Fourier transformation of the interference lightintensity waveform measured at the step 200a. Numeral 200c designatesreverse Fourier transformation of the result obtained by the Fouriertransformation at the step 200b.

FIG. 5 is a block diagram illustrating the construction of the dataprocessing apparatus. In FIG. 5, reference numeral 2001 designates aninterference light intensity waveform measuring section for measuringthe interference light intensity waveform from the output of thedetector included in the photometry system. Numeral 2002 designates amemory for storing the measured result of the interference lightintensity waveform measuring part 2001. Numeral 2003 designates aFourier transformation means for Fourier transformation of the output ofthe interference light intensity waveform measuring part 2001 and of thedata from the memory 2002. Numerals 2004 and 2005 designate memories forstoring the Fourier transformed results from the Fourier transformationmeans 2003. Numeral 2006 designates a subtracter for obtaining thedifference between the output of the two memories 2004 and 2005. Numeral2007 designates a filter for filtering the output of the subtracter2006. Numeral 2008 designates a reverse Fourier transformation means forreverse Fourier transformation of the output of the filter 2007. Numeral2009 designates a burst interval measuring means for measuring the burstinterval from the output of the reverse Fourier transformation means2008.

The operation of the apparatus is described with reference to FIGS. 4(b)and 5. First of all, the sample is irradiated with the interferencelight flux emitted from the Michelson interferometer 13 and the lightreflected by the sample is received by the photodetector included in thereflection light photometry system 26. The received light is convertedinto an electrical signal as an interference light intensity waveform(at step 200a).

This interference light intensity waveform is Fourier transformed (atstep 200b) and is subjected to a predetermined filtering process and thefiltered result is reverse Fourier transformed to produce a Spatialgram(at step 200c). From the interval between burst peaks in thisSpatialgram, the thickness of a layer is determined.

The interference light intensity waveform including the thicknessinformation for the thin multi-layer film is measured by theinterference light intensity waveform measuring part 2001 from theelectrical signal that is forwarded from the detector in the photometrysystem. This interference light intensity waveform is Fouriertransformed by the Fourier transformation means 2003, resulting in aspectrum. Prior to the measurement of the interference light intensitywaveform for the sample, the interference light intensity waveform dataare measured by the same method on a standard sample which is producedby, for example, evaporating gold on a semiconductor substrate and thesedata are stored in the memory 2002. Then, the interference lightintensity waveform data of the standard sample are read out from thememory 2002 as required and Fourier transformed, resulting in thespectrum. The spectrum of the thin multi-layer film sample and thespectrum of the standard sample are stored in the memories 2004 and2005, the contents of the memories are input to the subtracter 2006 toobtain a difference spectrum, and the difference spectrum in the noisewavenumber band is subjected to filtering in the filter 2007 to removenoise. The difference spectrum obtained is reverse Fourier transformedby the reverse Fourier transformation means 2008, thereby producing aSpatialgram called a Kepstrum. In the Kepstrum, there are bursts becauseall the respective reflected light components are intensified byinterfering with each other at positions where the optical path lengthdifferences due to differences between the positions of the movingmirror coincide with the optical path length differences between therespective reflected light components from the sample. These distancesbetween respective bursts correspond to the optical path lengthdifferences between respective reflection light components. Accordingly,by measuring the distance between the bursts with the burst intervalmeasuring means 2009, the optical path length differences and thethicknesses of respective layers are obtained.

By performing the waveform analysis on the Kepstrum obtained utilizingthe Fourier analysis, the thicknesses of respective layers of the thinmulti-layer film are obtained.

This prior art film thickness measuring method employing the FTIR methodwill be described with reference to FIG. 10 showing a conceptual diagramof the optical system. In FIG. 10, reference numeral 10 designates alight source emitting light irradiating a sample. Reference numeral 12designates a non-spherical mirror converting the light from the lightsource 10 into a parallel light beam. Numeral 14 designates a beamsplitter for dividing the parallel light beam from the non-sphericalmirror 12 into two parts. Reference numeral 15 designates a fixed mirrorreflecting the light transmitted through the beam splitter 14. Referencenumeral 16 designates a moving mirror reflecting the light reflectedfrom the beam splitter 14. Numeral 17 designates a driver for scanningthe moving mirror 16 at a constant speed. Reference numeral 13designates a Michelson interferometer generating an interference lightflux and comprising the beam splitter 14, the fixed mirror 15, themoving mirror 16, and the driver 17.

Reference numeral 27 designates an aperture for limiting the magnitudeof the interference light from the beam splitter 14 of the Michelsoninterferometer 13. Reference numeral 28 designates a plane mirrorreflecting the parallel light beam from the aperture 27 to change itsdirection. Reference numeral 11 designates a sample irradiated by theparallel light beam from the plane mirror 28. Reference numeral 29designates a plane mirror reflecting the parallel light beam reflectedfrom the sample 11 to change its direction. Reference numeral 30designates a non-spherical mirror on which the parallel light beam fromthe plane mirror 29 is incident. Reference numeral 21 designates adetector for detecting the light collected by the non-spherical mirror30. Reference numeral 26 designates a reflection photometry system formetering the sample comprising the aperture 27, the plane mirror 28, thesample 11, the plane mirror 29, and the non-spherical mirror 30.

The light emitted from the light source 10 is converted into a parallellight beam by the non-spherical mirror 12 and is introduced into theMichelson interferometer 13. The Michelson interferometer 13 includesthe beam splitter 14 for dividing the incident parallel light beam intotwo parts, the fixed mirror 15 reflecting the light transmitted by thebeam splitter 14, and the moving mirror 16 reflecting the lightreflected from the beam splitter 14 which is scanned at a constant speedby the driver 17. The transmitted light and the reflected light of thebeam splitter 14 are respectively reflected by the fixed mirror 15 andthe moving mirror 16 and again returned to the beam splitter 14 andsynthesized on that plane to interfere with each other. Thisinterference light is an interference light flux that is modulated intime by the constant speed scanning of the moving mirror 16 and exits atthe side of the aperture 27 for reflection photometry. The parallellight beam from the Michelson interferometer 13 is reformed to anarbitrary magnitude by the aperture 27 and then changes direction at theplane mirror 28. This parallel light beam irradiates the surface of thesample 11. The light reflected from the sample 11 is subjected tointerference due to the multiple film construction of the sample 11,changes its direction at the plane mirror 29, and is collected on thelight receiving surface of the detector 21 by the non-spherical mirror30.

FIG. 6 shows the reflection light paths of one-dimensional lightreflected at respective layers of the light flux incident on the sampleby the reflection photometry system of the Michelson interferometershown in FIG. 10. In FIG. 6, reference numeral 1 designates asemiconductor substrate and reference numerals 2, 3, and 4 designatethin semiconductor films successively laminated on the semiconductorsubstrate 1 in this order. Reference numeral 5 designates light incidenton the sample from the Michelson interferometer. Numeral 6 designateslight reflected from the surface of the thin semiconductor film 4 at theuppermost layer of the sample. Numeral 7 designates light reflected atthe interface between the thin semiconductor film 4 and the thinsemiconductor film 3. Numeral 8 designates light reflected at theinterface between the thin semiconductor film 3 and the thinsemiconductor film 2. Numeral 9 designates light reflected at theinterface between the thin semiconductor film 2 and the semiconductorsubstrate 1.

Suppose that the film thicknesses and refractive indices of the thinsemiconductor films 2, 3, and 4 are respectively, (d₁, n₁), (d₂, n₂),and (d₃, n₃) and the refractive index of the substrate 1 is n_(s). Thelight reflected by respective layers produces phase differences due todifferent respective optical path lengths and are synthesized at thesurface of the sample 11 and interfere with each other. The optical pathlength difference δ_(i) of the reflected light component reflected atthe interface between the i-th layer and (i+1)-th layer for thereflected light component 5 at the surface of the sample 11 is given bythe following formula (1). ##EQU1## The thicknesses of the respectivelayers are obtained from an analysis of the interference light intensitywaveform of the reflected light utilizing the phase difference on thebasis of the δ_(i).

Generally, a method of evaluating layer thickness from the analysis ofthe interference fringes of the reflected interference spectrum of athin film is adopted. This method is effective in a case where the filmcomprises a single layer. However, when the film comprises a pluralityof layers, it is quite difficult and not practical to separate andanalyze each of the fringes. Therefore, the Fourier analysis isutilized, i.e., the film reflection interference spectrum is filtered toremove noise, and the filtering result is reverse Fourier transformed toobtain a Spatialgram corresponding to the moving distance of the movingmirror 16. In the Spatialgram, respective bursts appear because all thelight beams intensify each other by interference at positions where theoptical path difference corresponding to the scanning position of themoving mirror 16 coincides with the optical path length difference ofrespective reflection light components. This intensification isrepresented in formula (1), and the distances between respective burstscorrespond to the optical path length differences between respectivereflected light beams.

FIG. 11 shows a Spatialgram obtained from the reflected light shown inFIG. 6. The abscissa represents the position of the moving mirror 16 andthe ordinate represents reflected light interference intensity. In thefigure, the center burst 31 corresponding to the reflected lightcomponent 6 at the surface of the sample 11 appears as the origin andthe symmetrical reflected light components 7, 8, and 9 of respectivelayers produce respective side burst peaks 32, 33, and 34. Provided thatthe distances from the center burst 31 to the respective side burstpeaks are Li (i=1, 2, 3), an optical path length difference δ_(i)between the respective reflected light components coincides with 2L_(i),a sum of the incident path and the reflected path to and from the movingmirror 16. Therefore, the following equation is obtained from theabove-described formula (1): ##EQU2##

By performing a waveform analysis of the Kepstrum that is obtained byreverse Fourier transformation of the reflected interference light ofthe multi-layer film, it is possible to obtain thickness information forthe respective layers of the multi-layer film.

However, in this prior art method, the thin film measurement limit(d_(limit)) is determined by the formula (3) according to the photometrywavenumber range Δ.

    d.sub.limit =1/(2·Δ·n)             (3)

This is equivalent to the fringe interval in the interference wavenumberin wavenumber (or wavelength) space of the single layer film having athickness d and a refractive index n, corresponding to 1/(2·d·n) andshows that the thickness separation limit in the Spatialgram for amulti-layer film requires information on the interference components ofrespective films corresponding to one interference fringe in wavenumberspace.

Accordingly, the thickness measuring limit of a thin film is determinedby the photometry wavenumber range that, in turn, is determined by thephotometry system and the absorption of the material of the measuredmulti-layer film.

With respect to the transmission characteristics of the light of thephotometry system, Japanese Published Patent Application Hei. 5-302816discloses a system that is responsive to a wider wavenumber rangebecause of an improvement in the optical parts and employment ofcomposite materials having different transmission wavenumber bands. Forexample, a light source, an optical system, and a light receiving partfor common use have wavenumber characteristic ranges mutuallyoverlapping each other.

FIG. 12(a) shows construction of an optical detector in a thinsemiconductor multi-layer film thickness measuring apparatus having alight source, an optical system, and a light detector for common usethat have wavenumber characteristic ranges mutually overlapping eachother. In the figure, reference numeral 21a designates a beam splitterfor splitting the light beam collected by the light collecting mirror.Reference numerals 21b and 21c designate a mercury cadmium telluride(MCT) detector and a silicon detector that convert the light divided bythe beam splitter 21a into an electrical signal. Reference numeral 21ddesignates an electrical signal synthesizer circuit for synthesizingelectrical signals obtained from the MCT detector 21b and the silicondetector 21c, respectively.

By constructing the photodetector as such, the detection sensitivity ofthe detector amounts to the sum of the sensitivity characteristics ofthe MCT detector and the silicon detector, whereby sensitivitycharacteristics that cannot be achieved with a single photodetector areobtained.

As shown in FIG. 12(b), the MCT detector 21b can be replaced by a lowcost tri-glycine sulfate (TGS) detector 21e. In this case, since partsfor cooling the MCT detector are not required, the apparatus issimplified and cost is reduced.

FIG. 13 shows an improvement of the photodetector shown in FIG. 12(a).The MCT detector 21b and the Si detector 21c are fixed in the same planewith epoxy resin or the like in a liquid nitrogen cooler 50 that coolsthe MCT detector 21b. A light beam collected by a collecting mirror 30enters directly into both the MCT detector 21b and the Si detector 21cand is detected at the same time. Then, the electrical signals outputfrom the detectors are synthesized in the electrical signal synthesizercircuit 21d.

Employing such a construction, influences due to the transmissioncharacteristic of the beam splitter disappear and the photometricwavenumber ranges of both the detectors 21b and 21c are obtained moreimmediately, improving the photometry precision.

In FIG. 14, three kinds of photodetectors are employed as a complexphotodetector. By arranging a germanium (Ge) detector 44 in the sameplane as the MCT detector 21b and the Si detector 21c, the sensitivityvalley of the synthesized sensitivity characteristic of the MCT detector21b and Si detector 21c is compensated. It is desirable to employ an MCTdetector having a larger area than the other detectors because the MCTdetector 21b is inferior in sensitivity to other detectors. Such aconstruction provides a photodetector having a high sensitivity and awide photometric wavenumber range.

FIG. 15 is a chart of wavenumber characteristic ranges of various kindsof light sources, photodetectors, and beam splitters. According to thesum of the wavenumber characteristic ranges of both the MCT detector andthe Si detector, the possibility of detection over a wide range fromaround 25000 cm⁻¹ to 500 cm⁻¹ is presented. This suggests that light ina range from visible light (blue light) to far infrared light ispossibly detected by a complex photodetector incorporating an MCTdetector and an Si detector for optimization. In FIG. 15, subscripts A,B, and C in parentheses represent photodetectors comprising the samematerials but with different composition ratios.

FIGS. 16(a) and 16(b), respectively, show light transmission memberscorresponding to the beam splitter. In both FIGS. 16(a) and 16(b),reference numeral 54 designates a region comprising calcium fluoride(CaF₂) and numeral 55 designates a region comprising quartz (SiO₂). Byemploying two materials having different light transmission bands forrespective halves of the light transmission area of the beam splitter,the characteristic wavenumber range of the beam splitter is enlarged tothe sum of the respective characteristic wavenumber ranges of the twomaterials. In the above-described construction, according to the columnof the beam splitter in the table of FIG. 15, the aggregate wavenumbercharacteristic range of the beam splitter employing calcium fluoride(CaF₂) and quartz (SiO₂) is approximately from 25000 cm⁻¹ to 2000 cm⁻¹.In addition, the construction of FIG. 16(b) having more than twodifferent materials for the respective sectioned areas arrangedalternatingly can reduce the destruction of wavefronts of a transmittedlight beam to a larger extent than the construction of FIG. 16(a) havingtwo different materials for the half-sectioned areas, thereby providinga more uniform inplane beam intensity.

The beam splitter may comprise three materials as shown in FIG. 16(c).In the construction of FIG. 16(c), a calcium fluoride (CaF₂) region 54,a quartz (SiO₂) region 55, and a potassium bromide (KBr) region 52 arearranged at the triple-sectioned areas of the light transmission region.According to the beam splitter column of FIG. 15, the beam splitterincluding calcium fluoride, quartz, and potassium bromide enablesoptical measurement in a wavenumber range of approximately from 25000cm⁻¹ to 400 cm⁻¹, thereby enlarging the long wavelength band to a largerextent than the construction employing two materials shown in FIGS.16(a) and 16(b).

In addition, a system in which the light source is improved as shown inFIG. 17 may be employed. In FIG. 17, light beams from a tungsten halogenlamp 10a and a nichrome luminous lamp 10c are collected by collectingmirrors 10b and 10d, respectively, and are synthesized through a beamsplitter 10e. The synthesized beam is reformed by an aperture 10f as acollected light source and introduced to the collimating mirror 12.Since the optical path lengths from the aperture 10f to the respectivelamps 10a and 10c are equal to each other, the respective light beamsfrom the lamps that are synthesized at the beam splitter 10e have thesame wavefronts at the aperture 10f and become one parallel light beamat the collimating mirror 12.

By combining the tungsten halogen lamp 10a and the nichrome luminouslamp 10c and synthesizing the outgoing light, it is possible toirradiate a sample with a light beam of the wavenumber range from 25000cm⁻¹ to 200 cm⁻¹ as shown in the light source column of FIG. 15.

Japanese Published Patent Application Hei. 3-110405 discloses animprovement in which the light irradiates a substrate as a parallellight beam, whereby the variation in the light incident on the sampleand variations in the incident surface are reduced, and a Kepstrumincluding correct information for the thin multi-layer film is obtained,as shown in FIG. 10.

Japanese Published Patent Application Hei. 4-66806 discloses a dataprocessing apparatus for processing a signal that is converted into anelectrical signal by a light detector. In this apparatus, the measuredphotometered spectrum to be subjected to a Fourier transformation issupplemented with data of a constant value in the wavenumber bandsexceeding the high band side and the low band side, whereby generationof a quasi-peak is suppressed.

FIG. 18 shows a flowchart illustrating the content of the processingperformed by the data processing apparatus supplementing data of aconstant value prior to the Fourier transformation. In FIG. 18, the filminterference spectrum is measured by the FTIR apparatus according to aconventional method (at step 100a). The low frequency component includedin the thus obtained spectrum is removed (at step 101a), resulting in afilm interference spectrum as shown in FIG. 19.

In this embodiment, spectrum data that is obtained by processing thewaveform data (at step 101b) is added. More particularly, as shown inFIG. 20, the reflection interference spectrum intensity data at the leftside (wavenumber σ₁ =12000 cm⁻¹) of the interference spectrum issupplemented as interference spectrum intensity data from O to σ₁ cm⁻¹,and the spectrum intensity data of the right side end in the figure(wavenumber σ₂ =12000 cm⁻¹)) is supplemented as reflection interferencespectrum intensity data from the wavenumber σ_(max) cm⁻¹.

Subsequently, the reflection interference spectrum data after thewaveform data processing is performed that is shown in FIG. 20 isFourier transformed (at step 101c), thereby producing a Spatialgram asshown in FIG. 21 (at step 101d). The peaks of this Spatialgram aresearched (at step 101d) and, from the interval between the peaks, thelayer thickness is calculated (at step 101f).

When the Spatialgram shown in FIG. 21 is compared with a Spatialgramthat is obtained without such data supplementation, although thereflection interference spectrum of the same wavenumber range isobtained from the same semiconductor triple-layer film, the side burstscorresponding to respective film thicknesses are significantlyclarified, whereby quasi-peaks are suppressed to a great extent.

FIG. 22 shows a power spectrum corresponding to the Spatialgram shown inFIG. 21. Of course, even in FIG. 22, the peak values I, II, and IIIrepresenting respective film thicknesses are much clarified and there isno obstacle to the automation of the thickness measuring operation.

Even when the Spatialgram shown in FIG. 21 is compared with aSpatialgram that is obtained without performing such data interpolation,the position of the side burst in the abscissa does not change at all.Therefore, even when the reflection interference spectrum of arelatively narrow wavenumber range is employed, an accurate thicknessmeasurement can be performed.

Japanese Published Patent Application Hei. 4-120404 discloses subjectinga reflection spectrum that is obtained by Fourier transformation to acomplex power reverse Fourier transformation, thereby clarifying thepeaks by making all the burst waveforms of the same phase, wherebythickness measuring precision is improved. FIG. 23 shows a flowchartillustrating the content of the processing performed by data processingapparatus including such a complex power reverse Fourier transformation.

In FIG. 23, reference numeral 150 designates an optical system thatcontinuously irradiates a sample with interference light flux havingdifferent wavenumbers, the sample including a thin semiconductormulti-layer film. The interference light flux reflected from the sampleis detected to produce an interferogram. Reference numeral 110designates a Fourier transformation means for Fourier transformation ofthe interferogram that is obtained by converting the light signal withthe photodetector included in the optical system 150 to obtain areflected light spectrum. Reference numeral 120 designates a filter forfiltering the Fourier transformed signal that is obtained from theFourier transformation means 110. Reference numeral 130 designates acomplex power reverse Fourier transformation means for performing acomplex power reverse Fourier transformation on the reflection spectrumthat is obtained by filtering with the filter 120 to obtain a spaceinterference waveform.

In this embodiment, the reflection spectrum that is obtained byfiltering is subjected to the complex power reverse Fouriertransformation by the complex power reverse Fourier transformation means130 to obtain a space interference intensity waveform.

This complex power reverse Fourier transformation means 130 produces thespace interference intensity waveform in the reverse Fouriertransformation employing the composite power transformation including acosine term and a sinusoidal term as represented by the formula (4):##EQU3##

Next, the thickness of the sample comprising a thin semiconductormulti-layer film on a semiconductor substrate is measured and evaluated.The sample comprises a GaAs substrate on which Al_(x) Ga_(1-x) As(x=0.5, 0.85 μm thick) , Al_(x) Ga_(1-x) As (x=0.1, 0.1 μm thick) , andAl_(x) Ga_(1-x) As (x=0.5, 1.4 μm thick) are grown. A space interferenceintensity waveform obtained by the complex power reverse Fouriertransformation means 130 is shown in FIG. 24. In the conventional cosinereverse Fourier transformation, two burst waveforms overlap each otherto produce an asymmetrical waveform so that it is difficult to find thepeak position. In addition, since this asymmetrical waveform issensitive to the filter condition in the reverse Fourier transformationand changes its shape, it is actually impossible to find the peak inthis waveform and to obtain the layer thicknesses.

On the other hand, in the space interference waveform shown in FIG. 24,although the peak position interval corresponds to 0.1 μm, the burstwaveforms are clearly separated and a spatial interference intensitywaveform that is sufficiently stable for an actual thickness measurementis obtained.

Since the space interference intensity waveform obtained by the complexpower reverse Fourier transformation includes more information than thatobtained by the conventional cosine reverse Fourier transformation andrespective burst waveforms all have the same phases, the precision ofthe thickness measurement is increased. For example, in a photometeringcondition having a measurement limit of 0.2 μm, a thickness measurementof a 0.1 μm thickness is possible.

Regardless of the above-described efforts, the high frequency lighttransmission limit ν_(h) is determined by the band edge absorption ofthe semiconductor material to be measured while the low frequency limitν₁ is determined by the crystalline lattice vibration absorption,thereby limiting the measured light wavenumber range Δ=ν_(h) -ν_(l)which results in a physical limit in the precision of d_(limit). Forexample, the band edge absorption wavenumber of Al_(x) Ga_(1-x) As(x=0.45) is 16500 cm⁻¹, the lattice vibration absorption is about 1500cm⁻¹, so Δ becomes 15000 cm⁻¹. When this Δ is applied in the formula(3), the d_(limit) is about 0.1 μm. In other words, in the prior arttechnique, the thin film measuring limit is determined by the absorptionof the semiconductor material, resulting in a limitation in thethickness measurement of about 0.1 μm.

SUMMARY OF THE INVENTION

It iS an object of the present invention to provide an apparatus and amethod for measuring the thicknesses of layers of a thin semiconductormulti-layer film utilizing infrared light interference fornon-destructively measuring the thicknesses of respective layers of thethin multi-layer film with a sub-micron precision and without contact.

Other objects and advantages of the present invention will becomeapparent from the detailed description given hereinafter; it should beunderstood, however, that the detailed description and specificembodiments are given by way of illustration only, since various changesand modifications within the scope of the invention will become apparentto those skilled in the art from this detailed description.

According to the present invention, an apparatus for measuring thethickness of the layers of a thin semiconductor multi-layer filmincludes means for irradiating a multi-layer semiconductor film withlight having a wavenumber range from visible light to infrared, meansfor measuring the multi-layer thickness employing a Fouriertransformation thickness measuring method that measures respective layerthicknesses from a waveform analysis of a Spatial interference waveformthat is obtained from the Fourier transformation of film interferencecomponents included in light reflected from the film, means for settingrespective measured values of thicknesses obtained from the waveformanalysis of the Spatial interference waveform as initial values, meansfor obtaining a film interference waveform of one of a wavenumberdispersion spectrum and a wavelength dispersion spectrum of reflectedlight from a numerical calculation using an optical characteristicmatrix, and a data processing apparatus for obtaining respectivethicknesses from waveform fitting of the calculated values with themeasured values.

Since the indefinite measuring value of the thickness of the upper layeror lower layer is intentionally changed to detect the optimum fittingwaveform, even when the interference fringes are included for less thanone-half of the thin film portion in the measuring wavenumber range, itis possible to fit the interference waveform for all of the multi-layerfilm and measure the thickness of a thin film that is not limited to themeasuring wavenumber range.

According to a first aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includes afirst memory storing refractive index distribution and wavenumberdispersion data of respective layers of a multi-layer film, aspectroscopic apparatus for spectroscopically measuring successively thereflected light from the lower layer in a range from visible light tofar infrared light, film interference spectrum operating means forforming an interference spectrum from the spectrum measured by thisspectroscopic apparatus by removing the optical transmittingcharacteristic of the spectroscopic apparatus to take out only amulti-layer film interference component, a second memory for storing theinterference spectrum that is obtained by taking out only themulti-layer interference component that is produced by the filminterference spectrum operating means, Spatialgram calculating means forcalculating the Spatialgram by reverse Fourier transforming only thesensitivity wavenumber band of the interference spectrum from which theoptical transmitting characteristics of the spectroscopic apparatus areremoved, a third memory for storing the Spatialgram that is calculatedby this Spatialgram calculating means, film thickmess approximate valuecalculating means for calculating the side burst peak position of theSpatialgram and approximate values of respective film thicknesses byreading out the refractive index distribution of respective layers fromthe first memory, a fourth memory for storing the approximate values ofrespective thicknesses that are calculated by this film thicknessapproximate value calculating means, theoretical interference spectrumcalculating means for calculating the theoretical interference spectrumusing a characteristic matrix calculation on the basis of the refractiveindex distribution and wavenumber dispersion data of respective layers,and recalculating means for changing the film thickness set values ofrespective layers to minimize the difference between the interferencespectrum and the theoretical interference spectrum and recalculating thetheoretical interference spectrum to assume the real film thickness.Accordingly, by obtaining approximate layer thicknesses, producingtheoretical interference spectrum waveforms from numerical calculationsusing the optical characteristic matrix, and waveform fitting with theoriginal interference spectrum waveform while changing the layerthickness, it is possible to improve thickness measuring precision.

According to a second aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includes aspectroscopic apparatus including a light source emitting measuringlight, an interferometer producing interference light from the lightfrom the light source that is modulated in time, an optical systemincluding a light transmitting material for introducing the interferencelight to the sample to be measured and including a thin multi-layer filmon a substrate, and a Michelson interferometer having a light detectingpart for detecting the reflected interference light from the film.

According to a third aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includes alight detecting part including a plurality of photodetectors havinglight measuring wavenumber bands overlapping each other, whereby thelight detecting sensitivity of the reflected light from the sample isincreased and a more exact thickness calculation is obtained.

According to a fourth aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includes alight transmitting member including a plurality of unit members havingtransmission wavenumber bands overlapping each other, whereby thein-plane intensity of the measuring light incident on the sample is madeuniform, a more exact measuring light is obtained, and a more exactthickness calculation is obtained.

According to a fifth aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includes alight source that has a plurality of unit light sources emitting lightof different wavelengths that are optically synthesized to produce ameasuring light, whereby photometering over a wide wavenumber range anda more exact thickness calculation are obtained.

According to a sixth aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includes anoptical system that irradiates the sample with interference light as alight beam having a prescribed beam width and variations in the angle ofthe test light incident on the surface of the material and variations inthe incident plane are reduced, whereby a Kepstrum of high precision isobtained and a more exact film thickness calculation is achieved.

According to a seventh aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includesfilm interference spectrum operating means that processes aninterference spectrum by supplementing the wavenumber range exceeding aphotometering spectrum wavenumber range with constant values whileproducing the interference spectrum, whereby film thickness informationcan be obtained from the reflection interference spectrum of arelatively narrow wavenumber range and, on that basis, a more exactthickness calculation is achieved.

According to an eighth aspect of the present invention, a thinsemiconductor multi-layer film thickness measuring apparatus includesSpatialgram calculating means for performing a composite power reverseFourier transformation, whereby a more exact and stable measurement ofthe thickness of respective layers of the thin multi-layer film can beperformed in a prescribed photometering wavenumber range and, on thatbasis, a more exact thickness calculation is obtained.

According to a ninth aspect of the present invention, a film thickmessmeasuring method employed in a thin semiconductor multi-layer filmthickness measuring apparatus includes irradiating a semiconductormulti-layer film with light having wavenumbers in a range from visiblelight to infrared, measuring the multi-layer thickness employing aFourier transformation film thickness measuring method measuringrespective film thicknesses from a waveform analysis of the Spatialinterference waveform obtained from the Fourier transformation of theinterference components included in the reflected light, settingrespective measured values of film thickness obtained from the waveformanalysis of the Spatial interference waveform as initial values,obtaining a film interference waveform of one of a wavenumber dispersionspectrum and a wavelength dispersion spectrum of reflected light, bynumerical calculation using an optical characteristic matrix, andobtaining respective thicknesses of high precision from waveform fittingof calculated values with measured values. By this construction, in thewaveform fitting comparing the power reflectivity obtained by thenumerical calculation utilizing the optical characteristic matrix withthe interference waveform from an actual measurement, the measuredvalues of the thicknesses of the layers of the thin film and the upperlayer or the lower layer having indefinite values are deliberatelychanged to detect the optimum fitting waveform. Therefore, even whenonly one-half the interference fringe of the thin film part is includedin the measuring wavenumber range, waveform fitting of the interferencewaveform of the entire multi-layer film is achieved and measurement ofthe thickness of a layer is not limited to the measuring wavenumberrange.

According to a tenth aspect of the present invention, in a filmthickness measuring method employed in a thin semiconductor multi-layerfilm thickness measuring apparatus, the refractive index dispersion andthe wavenumber dispersion data of respective layers of the multi-layerfilm are stored, the reflected light from the lower layer film issuccessively spectroscopically measured in a range from visible light tofar infrared light with a spectroscopic apparatus, the opticaltransmission characteristic of the spectroscopic apparatus is removedfrom this spectrum to produce an interference spectrum including onlythe multi-layer film interference component, the interference spectrumincluding only the multi-layer film interference component is stored,only the sensitivity wavenumber band of the interference spectrum fromwhich the optical transmission characteristic of the spectroscopicapparatus is removed is reverse Fourier transformed to calculate aSpatialgram, this Spatialgram is stored, the side burst peak position ofthe Spatialgram is read out to calculate the approximate value ofrespective film thicknesses, these approximate values of respective filmthicknesses are stored, the theoretical interference spectrum isobtained from a characteristic matrix calculation performed on the basisof approximate film thickness data, the refractive index distribution,and wavenumber dispersion data of respective layers, the film thicknessset values of respective layers are changed to minimize the differencebetween the measured interference spectrum and the theoreticalinterference spectrum, and the theoretical interference spectrum isrecalculated to assume the real film thickness with high precision.Accordingly, the apparatus produces approximate values of layerthicknesses, produces the theoretical interference spectrum waveformsfrom the numerical calculation of the optical characteristic matrix, andperforms waveform fitting with the original interference spectrumwaveform while changing layer thicknesses, thereby providing an enhancedmeasurement precision of layer thickness.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1(a) and 1(b) are diagrams illustrating a thin semiconductormulti-layer film thickness measuring apparatus according to a firstembodiment of the present invention in which FIG. 1(a) is a blockdiagram illustrating a schematic construction and FIG. 1(b) is aflowchart schematically illustrating operation.

FIG. 2 is a block diagram illustrating a detailed construction of thethin semiconductor multi-layer film thickness measuring apparatus ofFIG. 1(a).

FIG. 3 is a flowchart illustrating the operation of the recalculatingmeans of FIG. 2.

FIGS. 4(a) and 4(b) are diagrams illustrating a prior art thinsemiconductor multi-layer film thickness measuring apparatus in whichFIG. 4(a) is a block diagram showing a schematic construction and FIG.4(b) is a flowchart schematically showing operation.

FIG. 5 is a block diagram illustrating a detailed construction of thethin semiconductor multi-layer film thickness measuring apparatus ofFIG. 4(a).

FIG. 6 is a diagram illustrating the reflection light path of the lightreflected from the respective layers.

FIG. 7 is a film interference waveform in wavenumber space according toa thickness measuring example of a first embodiment of the presentinvention.

FIG. 8 is a Spatialgram obtained by reverse Fourier transformation ofthe interference waveform of FIG. 7 in a thickness measuring exampleaccording to the present invention.

FIGS. 9(a), 9(b), and 9(c) are diagrams illustrating the use ofnumerical calculation in fitting measured interference waveforms totheoretical forms according to an embodiment of the present invention.

FIG. 10 is a diagram illustrating the FTIR film thickness evaluatingapparatus disclosed in Japanese Published Patent Application Hei.3-110405.

FIG. 11 is a Spatialgram.

FIGS. 12(a) and 12(b) are diagrams illustrating the construction ofoptical detectors used in thickness measurement apparatus and employingcomposite photodetectors as disclosed in Japanese Published PatentApplication Hei. 5-302816.

FIG. 13 is a diagram illustrating a construction of another compositetype photodetector disclosed in Japanese Published Patent ApplicationHei. 5-302816.

FIG. 14 is a diagram illustrating a construction of still anothercomposite type photodetector disclosed in Japanese Published PatentApplication Hei. 5-302816.

FIG. 15 is a table of characteristic wavenumber ranges of the variouslight sources, photodetectors, and beam splitters disclosed in JapanesePublished Patent Application Hei. 5-302816.

FIGS. 16(a)-16(c) are diagrams illustrating composite type beamsplitters as a light transmitting material used in the semiconductorfilm thickness measuring apparatus disclosed in Japanese PublishedPatent Application Hei. 5-302816.

FIG. 17 is a diagram illustrating a construction of a light source ofthe semiconductor film thickness measuring apparatus disclosed inJapanese Published Patent Application Hei. 5-302816.

FIG. 18 is a flowchart illustrating the processing performed by the dataprocessing apparatus in the semiconductor film thickness measuringapparatus disclosed in Japanese Published Patent Application Hei.5-302816.

FIG. 19 is a diagram illustrating the film interference spectrum forprocessing according to FIG. 18.

FIG. 20 is a diagram illustrating the result obtained by performing theprocessing of FIG. 18 of the film interference spectrum shown in FIG.19.

FIG. 21 is a diagram illustrating the Spatialgram obtained by datainterpolation in the processing of FIG. 18.

FIG. 22 is a diagram illustrating a power spectrum corresponding to theSpatialgram shown in FIG. 21.

FIG. 23 is a flowchart showing the processing of the data processingapparatus in the semiconductor film thickness measuring apparatusdisclosed in Japanese Published Patent Application Hei. 4-120404.

FIG. 24 is a diagram illustrating a space interference waveform obtainedby the processing shown in FIG. 23.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiment 1

FIG. 1(a) illustrates an apparatus for measuring thicknesses of thelayers of a thin semiconductor multi-layer film according to a firstembodiment of the present invention.

In FIG. 1(a), reference numeral 13 designates a Michelson interferometergenerating an interference light flux. Reference numeral 26 designates aphotometry system for photometering the measuring light from theinterferometer 13 and irradiating a sample with that light flux.Reference numeral 150 designates a spectroscopic apparatus comprisingthe Michelson interferometer 13 and the photometry system 26 formeasuring the spectrum of the light reflected from the multi-layer film,continuously, from visible light to infrared light. Reference numeral100 designates a data processing apparatus for Fourier transforming theelectrical signal from the measured light generated by the photometrysystem 26 of the spectroscopic apparatus 150 and, specifically, by theoptical detector of the photometry system 26. A Michelson interferometerof a type in which a parallel light beam is incident on the sample, asshown in FIG. 10, is employed.

FIG. 1(b) shows a flowchart illustrating data processing performed bythis data processing apparatus 100. In this figure, reference numeral100a designates measuring the film interference spectrum, referencenumeral 100b designates Fourier transformation of the film interferencespectrum, and reference numeral 100c designates reverse Fouriertransformation of the result of the Fourier transformation. Referencenumeral 100d designates waveform fitting the result of the reverseFourier transformation by comparing the measured and calculatedinterference spectrum waveforms.

FIG. 2 is a block diagram illustrating an embodiment of the dataprocessing apparatus 100. In the figure, reference numeral 1001designates a film interference spectrum operating means for removing theoptical transmission characteristic of the spectroscopic apparatus fromthe spectrum to leave only the multi-layer film interference components.Reference numeral 1002 designates a second memory means for storing theinterference spectrum of the multi-layer film interference componentsfrom the film interference spectrum operating means. Reference numeral1003 designates a Spatialgram calculating means for reverse Fouriertransformation of only the sensitive wavenumber band of the interferencespectrum to obtain a Spatialgram. Reference numeral 1004 designates afirst memory means for storing refractive index distribution andwavenumber dispersion data of the multi-layer film. Reference numeral1005 designates a third memory means for storing data calculated by theSpatialgram calculating means 1003. Reference numeral 1006 designates alayer thickness approximate value calculating means for reading out therefractive indices and wavenumber dispersion data of respective layersof the multi-layer film stored in the first memory means 1004 and theside burst peak positions of the Spatialgram stored in the third memorymeans 1005 to obtain approximate values of respective layer thicknesses.Reference numeral 1007 designates a fourth memory means for storing theapproximate value of the layer thicknesses calculated by the layerthickness approximate value calculating means 1006. Reference numeral1008 designates a theoretical interference spectrum calculating meansfor calculating the theoretical interference spectrum using acharacteristic matrix calculation based on the layer thicknessapproximations. Reference numeral 1009 designates a recalculating meansfor comparing the actual measured value of the interference spectrum andthe theoretical interference spectrum and changing the layer thicknessesof respective layers to minimize the difference between both spectra andrecalculating the theoretical interference spectrum.

The thin semiconductor multi-layer film measuring apparatus of thisfirst embodiment combines the burst peak analysis method using aSpatialgram and the fringe waveform analysis method using aninterference waveform in the wavenumber (wavelength) space so as tocombine their advantages and compensate for their disadvantages.

More particularly, firstly, in the burst peak analysis using theSpatialgram, the thickness of a layer can be measured by this method,the total thickness of a thin layer cannot be measured by this method,but the thicknesses of an upper and lower layer between the thin layerare measured.

Secondly, assuming the layer thickness information obtained at the firststep as an initial value, an interference waveform in wavenumber(wavelength) space is calculated applying the multi-layer filmreflection analysis method utilizing a series of optical characteristicmatrix methods. This result is fitted to the interference waveformobtained by a measurement employing the thickness of the thin layer andthe thicknesses of upper and lower layers, which are indefinite, asparameters, whereby the thickness of the thin layer that cannot bemeasured in the first step is obtained.

In this embodiment, waveform fitting makes the power reflectivityobtained by the numerical calculation employing an opticalcharacteristic matrix coincide with the interference waveform of theactual measurement, and the measurements of the thin film and thethicknesses of the upper and lower layers that are indefinite arechanged intentionally to find the optimum fitting waveform, to increasethe precision of the measurement of the layer thickness. Therefore, evenwhen less than one interference fringe of the thin film portion isincluded in the measurement wavenumber range, waveform fitting of theinterference waveform of the entire multi-layer film is enabled, wherebythe measurement of a layer thickness is not limited to within themeasurement wavenumber range.

A description is given of the operation with reference to FIGS. 1(a),1(b), and 2. First of all, the interference light flux irradiating thesample from the Michelson interferometer 13 is received by thephotodetector included in the reflection photometry system 26 andconverted into an electrical signal.

The electric signal converted by this photodetector is input to the dataprocessing apparatus 100, in which the film interference spectrum ismeasured (at step 100a), the measured result is Fourier transformed (atstep 100b), a prescribed filtering process is performed, and thefiltered result is reverse Fourier transformed to obtain a Spatialgram(at step 100c). Then, the thickness of a layer is obtained from thespacing of the burst peaks in the Spatialgram. By carrying out anoptical characteristic matrix operation on the basis of the approximatevalue of the layer thickness, a theoretical interference spectrum isobtained, waveform fitting between the theoretical interference spectrumand the actual measured interference spectrum is performed, varying thelayer thickness by a predetermined increment, and a layer thickness thatproduces a theoretical interference spectrum that is closer to thewaveform configuration of the actual measured value is obtained (at step100d).

A detailed description is given of the processing of this dataprocessing apparatus. First of all, the light reflected from themulti-layer film on the sample is spectroscopically measuredcontinuously over a range from visible light to far infrared light bythe spectroscopic apparatus and the optical transmission characteristicof the spectroscopic apparatus is removed from the spectrum by the filminterference spectrum operating means 1001 to obtain only themulti-layer film interference component. The interference spectrum onthe multi-layer interference component obtained by the film interferencespectrum operating means 1001 is stored in the second memory means 1002and only the sensitive wavenumber region of this interference spectrumis reverse Fourier transformed by the Spatialgram calculating means 1003to produce the Spatialgram. The data calculated by the Spatialgramcalculating means 1003 is stored in the third memory means 1005.

The side burst peak position of the Spatialgram is obtained by the layerthickness approximate value calculating means 1006, the refractiveindices and the wavenumber dispersion data of respective layers of themulti-layer film are obtained from the first memory means 1004 to obtainapproximate respective layer thicknesses and to store them in the fourthmemory means 1007, and a theoretical interference spectrum is calculatedby the theoretical interference spectrum calculating means 1008 from thecharacteristic matrix calculation performed on the basis of theapproximate layer thickness data. Then, the recalculating means 1009compares the interference spectrum and the theoretical interferencespectrum, changes the thicknesses of respective layers to minimize thedifferences between the spectra, and makes the theoretical interferencespectrum calculating means 1008 recalculate the theoretical interferencespectrum.

FIG. 3 shows a flowchart illustrating the recalculating procedureperformed by the recalculating means. In the figure, reference numeral1009a designates setting the wavenumber. Reference numeral 1009bdesignates obtaining a square of the difference between the actualmeasured value and the calculated value of the film interferencewaveforms in respective wavenumbers. Reference numeral 1009c designatesobtaining a sum of the squares of the difference between the actualmeasured value and the calculated value of the film interferencewaveform in respective wavenumber ranges. Reference numeral 1009ddesignates obtaining the sum of the squares. Reference numeral 1009edesignates determination of whether the minimum value of the sum of thesquares is obtained. Reference numeral 1009f designates returning to thestep 1009a and increasing or decreasing the layer thickness by apredetermined increment when the minimum value of the sum of the squaresis not obtained. Reference numeral 1009g designates obtaining a layerthickness corresponding to the minimum value when the minimum value isobtained at the step 1009e.

FIGS. 9(a), 9(b), and 9(c) are diagrams illustrating film interferencewaveforms in wavenumber space that are obtained from measuring a threelayer structure of Al_(x) Ga_(1-x) As layers 2 to 4 (in layer 2, Alcomposition x is 0.45, in layer 3, x is 0.15, in layer 4, x is 0.45)that are successively laminated on the GaAs substrate shown in FIG. 6 bymeans of the prior art FTIR apparatus shown in FIG. 4. In FIG. 7, theinterference waveform is measured over the wavenumber range from 15500cm⁻¹ (point A in FIG. 7) to 2300 cm⁻¹ (point B in FIG. 7). FIG. 8 showsa Spatialgram that is obtained by reverse Fourier transformation of theregion from A to B of this interference waveform. In FIG. 8, the mixedcomposition ratios of the first layer 2 to the third layer 4 arerespectively 0.45, 0.15, and 0.45, the refractive indices arerespectively 3.27, 3.44, and 3.27, the calculated values of the layerthicknesses are respectively 0.484 μm, 0.069 μm, and 1.282 μm. In FIG.8, burst peaks corresponding to the interface reflection at therespective layers appear. However, the peak corresponding to thethickness (d₂ =0.55 μm) of the second layer 3 (x=0.15) overlaps with thepeak corresponding to the first layer (x=0.45, d₂ =0.43 μm) 2, and acorrect peak separation is not obtained.

In this embodiment, using the same processing performed by the prior artFTIR apparatus as described above, the film thickness information asshown in FIG. 8 is obtained and, in addition, by setting the filmthickness information obtained from the above processing as an initialvalue and performing a numerical calculation employing the opticalcharacteristic matrix using the formulae (4) to (7), the waveformconfiguration of the theoretical interference spectrum is obtained, andwaveform fitting of the waveform configuration of the theoreticalinterference spectrum to the waveform configuration of the actualmeasured interference spectrum is performed, thereby obtaining a moreexact thickness measurement of a layer of a thin multi-layer film.

When a multi-layer film of n layers is represented by an opticalcharacteristic matrix, assuming the optical characteristic matrix of then-th layer is M_(n) and the optical characteristic matrix of the nlayers is M^(n), the following equations apply. ##EQU4## β_(i) =2π·n_(i)·cosθ_(i) /λ(λ:wavelength of incident light)

P_(i) =n_(i) ·cosθ_(i) (θ_(i) :incident angle to the i-th layer)

n_(i-1) ·sinθ_(i-1) =n_(i) ·sinθ_(i)

n_(i) =n_(i) -jk_(i) (n_(i) :complex refractive index of i-th layer)

n_(i) :real refrative index of i-th layer

k_(i) :attenuation coefficient of i-th layer).

j: imaginary unit ##EQU5## r=amplitude reflectance σ=1/λ:wavenumber

    R(σ)=r·r.sup.* (8)

R=power reflectivity

r^(*) =complex conjugate of r

P_(B) =n_(s) ·cosθ_(s) (θ_(s) : incident angle to substrate)

n_(s) =n_(s) -jk_(s) (n_(s) : complex refractive index of substrate,

n_(s) : real refractive index of substrate,

k_(s) : attenuation coefficient of substrate) P_(o) =n_(o) ·cosθ_(o)

(θ_(o) : incident angle to substrate, n_(o) : refractive index of air).

When fitting of an interference waveform to these formulae (5) to (8)employing the parameters shown in the formula (9) for n=3, the result isshown in FIGS. 9(a) to 9(c). ##EQU6## m^(*) : effective mass of anelectron in a crystal ˜0.068 m_(o)

(m_(o) : mass of electron in vacuum, 9.11×,10⁻³¹ [kg])

N_(f) : carrier concentration in crystal ˜10¹⁷ cm⁻³ τ=m·μ/e

μ: mobility of a carrier in the crystal 300 [cm/V·S]

ε^(*) : relative dielectric constant of real part of crystal at highfrequency limit ˜12

ε_(o) : dielectric constant in vacuum=8.8542×10⁻¹² [F/m]

θi ˜5°.

This waveform fitting can be performed by the method as shown in FIG. 3.A wavenumber is set (at step 1009a), a square of the difference betweenthe actual measured value and the calculated value of the filminterference waveform in this wavenumber is obtained (at step 1009b),and a sum of the squared values at respective wavenumbers is obtained(at step 1009c). The sum of the squares is stored (at step 1009d), andwhether the minimum value of the squared sum is obtained is determined(at step 1009e). Then, the film thickness is increased or decreased at apredetermined interval (at step 1009f), and the processing is repeatedto obtain the minimum sum. Then, the layer thickness corresponding tothe minimum value of this sum is obtained (at step 1009g). This is thethickness of the triple layer film assumed in this embodiment.

The waveform fitting will be described with reference to FIG. 9. In FIG.9, the waveform shown by a wide line represents the film interferencewaveform obtained by actual measurement, and the waveform shown by anarrow line represents a film interference waveform calculated from theformulae (4) to (7). According to this FIG. 9, by converging thethickness of the second layer by gradually reducing the thickness from0.1 μm shown in FIG. 9(a) to 0.070 μm shown in FIG. 9(b), and further to0.053 μm shown in FIG. 9(c), the interference waveform of the entirethree layer film can be reproduced faithfully.

Accordingly, as shown in FIG. 3 described above, by decreasing orincreasing the thickness at a prescribed increment so that the sum ofthe squares of the differences between the calculated spectra and theactual measured spectra in respective wavenumber ranges is a minimumvalue, and finding the thickness at which the film interference waveformobtained by calculation and by actual measurement are closest to eachother, it is possible to determine precisely the thickness of the secondlayer and, further, the respective thicknesses of the first and thirdlayer that were impossible to measure by the prior art method aredetermined.

Although there is a little deviation between the theoretical, calculatedwaveform and the actually measured waveform shown in FIG. 9(c), bymaking efforts, such as using the waveform dispersion characteristic ofthe complex refractive indices of respective semiconductor crystals asmaterial constants, and data, such as free carrier absorption, close topractical values, further precision in waveform fitting can be realized.

In this way, according to this embodiment, on the basis of the Fouriertransformation infrared spectroscopic method, a semiconductormulti-layer film is irradiated with a light having a wavenumber rangefrom visible light to infrared and from waveform analysis of the spaceinterference waveform that is obtained by Fourier transformation of thefilm interference component in the reflected light, the thickness oflayers of the thin multi-layer film of a semiconductor device aremeasured employing a Fourier transformation thickness measuring method.The respective thickness values obtained from the waveform analysis ofthe space interference waveform are made initial values for obtainingthe film interference waveform of the wavenumber dispersion (wavelengthdispersion) spectrum of the reflected light employing a numericalcalculation using an optical characteristic matrix. This waveform isfitted to actual measured waveforms to obtain layer thicknesses withhigh precision. Therefore, even when only one interference fringe of thethin film part is included in the measuring wavenumber range, asufficient thickness resolution is obtained by waveform fitting of theinterference waveform of the entire multi-layer film, and a measurementthat was entirely impossible in the prior art method is achieved.

In other words, the splitting limit of the burst peak on the Spatialgramis as described above, determined by continuous photometry in thewavenumber range Δ that is determined by light transmissioncharacteristics of the optical system and the light absorption of themulti-layer film materials. This is equivalent to the wavenumbercorresponding to an inverse number of the optical path length of oneforward path of the infrared light propagation in the film (n·d) and itmeans that one or more fringes of the wavenumber (wavelength) Spatialinterference waveform of a thin monolayer are required to be included inthe measuring wavenumber range. According to this embodiment, in thewaveform fitting method of the (wavelength) Spatial interferencewaveform, by performing a Fourier transformation, the approximate valueof the film thickness is measured and the original interference fringeis accurately reproduced, utilizing the optical characteristic matrix,whereby the precision of the thickness measurement is improved.Therefore, even if only one-half an interference fringe of a thin filmis included in the measuring wavenumber range, a sufficient thicknessresolution is obtained in the waveform fitting of an interferencewaveform of the entire multi-layer film, thereby enabling a measurementthat was entirely impossible in the prior art method.

Although this method is a combination of the prior art techniques, thismethod cannot be realized from only each of respective techniques.

More particularly,

(1) In using only the fringe peak analysis method of the wavenumber(wavelength) Spatial interference waveform, a film thickness measurementof a multi-layer film of more than two layers is impossible.

(2) Even when the fitting of the wavenumber (wavelength) Spatialinterference waveform employing the optical characteristic matrixanalysis is tried, because the order of the layers of the multi-layerfilm and the initial values of the thicknesses of all the layers at thestart of the fitting are indefinite, the analysis is difficult and itspractice is impossible.

(3) The separation of the burst peak on the Spatialgram has a limit ofabout 0.1 μm due to the physical limitation described above.

In the above illustrated embodiment, since the parallel light flux isincident on the sample as described above, by irradiating a sample withthe measured light not focused toward the substrate but in a parallellight beam, variations in the incident angle on the sample andvariations in the incident plane are reduced. Thus, it is possible tocarry correct information of the thin multi-layer film into the obtainedKepstrum, whereby exact information is obtained for processing by thedata processing apparatus. Thus, improved thickness measuring precisionis achieved.

Embodiment 2

While in the above-described first embodiment the precision of thicknessmeasurement is improved by combining the FTIR method with aninterference waveform analysis in the optical characteristic matrixanalysis, by using those methods with wavenumber characteristic rangesoverlapping each other for improved light sources, optical systems, andlight detecting parts as shown in FIGS. 12 to 17, respectively, whichare disclosed in Japanese Published Patent Application Hei. 5-302816,the optical detection sensitivity of the FTIR method can be increased,whereby the film thickness measurement can be carried out exactly.

Embodiment 3

In the above-described second embodiment the precision of film thicknessmeasurement is improved by combining the FTIR method and theinterference waveform analysis employing optical characteristic matrixanalysis. As shown in FIG. 10 disclosed in Japanese Published PatentApplication Hei. 3-110405, when a photometering light beam that is notcollected on a substrate but irradiates the substrate as a parallellight beam is employed to reduce variations in incident angle andvariations in the incident plane, that light beam can include exactinformation of the thin multi-layer film in the obtained Kepstrum, andit is possible to increase the optical detection sensitivity of the FTIRmethod, thereby performing the thickness measurement accurately.

Embodiment 4

In the above-described second and third embodiments, the spectroscopicapparatus is improved to enhance the precision of the layer thicknessmeasurement. By employing a data processing apparatus that has improvedmeasurement precision by efficiently taking layer thickness informationfrom the reflection interference spectrum of a relatively narrowwavenumber band by Fourier transformation after adding data of aconstant value prior to the Fourier transformation as shown in FIGS. 18to 22 and disclosed in Japanese Published Patent Application Hei.4-66806, the measuring precision can be further increased.

Embodiment 5

In the above-described fourth embodiment the film thickness measurementprecision is enhanced by improving the Fourier transformation in thedata processing apparatus. By using a transformation that measures thethicknesses of respective layers of much thinner thin multi-layer filmsexactly and stably at a prescribed photometering wavenumber band byperforming a complex power reverse Fourier transformation as a reverseFourier transformation as shown in FIGS. 23 and 24 which are taken fromJapanese Published Patent Application Hei. 4-120404, the measuringprecision can be further increased.

Embodiment 6

By performing an interference waveform analysis employing the opticalcharacteristic matrix, combining the improvement of the reverse Fouriertransformation processing in the fifth embodiment and the improvement inthe interpolation of data in the fourth embodiment or the improvement ofthe optical system in the second and third embodiments, it is possibleto perform thickness measurements having a measurement limit of0.05+0.01 μm reliably. This limit is one-half of the measuringlimitation of 0.1 μm of the prior art method. Accordingly, even when theinterference fringe of the thin film part is only included by one-halfin this measuring range, a sufficient measurement of thickness of alayer can be performed.

What is claimed is:
 1. An apparatus for measuring thicknesses of layersin a thin semiconductor multi-layer film comprising:a first memory forstoring refractive index distribution and wavenumber dispersion data forrespective layers of a multi-layer film; a spectrometer for continuouslymeasuring spectral distribution of light reflected from an underlyinglayer of the multi-layer film over a range from visible light to farinfrared light; film interference spectrum operating means foreliminating optical transmission characteristics of the spectrometerfrom the spectral distribution measured by the spectrometer andproducing an interference spectrum including only multi-layer filminterference components; a second memory for storing the interferencespectrum including only multi-layer film interference componentsproduced by the film interference spectrum operating means; Spatialgramcalculating means for reverse Fourier transforming a wavenumber range ofan interference spectrum excluding the optical transmissioncharacteristics of the spectrometer and calculating a Spatialgram; athird memory for storing the Spatialgram calculated by the Spatialgramcalculating means; layer thickness approximate value calculating meansfor reading out side burst peaks of the Spatialgram and the refractiveindex distribution of respective layers stored in the first memory andcalculating approximate respective layer thicknesses; a fourth memoryfor storing the approximate respective layer thicknesses calculated bythe film thickness approximate value calculating means; theoreticalinterference spectrum calculating means for obtaining a theoreticalinterference spectrum from a characteristic matrix calculation based onthe approximate layer thicknesses, the refractive index distribution ofrespective films, and the wavenumber dispersion data stored in the firstmemory; and recalculating means for comparing the measured interferencespectrum with the theoretical interference spectrum, changing the layerthicknesses of the respective layers to lessen differences between themeasured interference spectrum and the theoretical interference spectrumand recalculating the theoretical interference spectrum to obtain layerthicknesses of high precision.
 2. The apparatus of claim 1 wherein thefilm interference spectrum operating means supplements a wavenumberrange exceeding the range of photometry with a constant value to producean interference spectrum.
 3. The apparatus of claim 1 wherein theSpatialgram calculating means employs a complex power reverse Fouriertransformation.
 4. A method for measuring the thicknesses of the layersof a thin semiconductor multi-layer film comprising:storing refractiveindex distribution and wavenumber dispersion data for respective layersof a multi-layer film; continuously spectrally analyzing light reflectedfrom an underlying layer of the multi-layer film over a range fromvisible light to far infrared light with a spectrometer; producing aninterference spectrum by eliminating an optical transmissioncharacteristic of the spectrometer from the spectrally analyzed light,leaving only multi-layer film interference components; storing theinterference spectrum of only the multi-layer interference components;calculating a Spatialgram from a reverse Fourier transformation for alimited wavenumber range of the interference spectrum from which theoptical transmission characteristic has been eliminated; storing theSpatialgram; reading out side burst peaks of the Spatialgram andrefractive index distribution of respective layers and calculatingapproximate respective layer thicknesses; storing the approximaterespective layer thicknesses; calculating a theoretical interferencespectrum from a characteristic matrix based on the approximate layerthicknesses, the refractive index distribution, and wavenumberdispersion data of respective layers; and comparing the interferencespectrum with the theoretical interference spectrum, changing the layerthicknesses of the respective layers to lessen differences between themeasured interference spectrum and the theoretical interference spectrumand recalculating the theoretical interference spectrum to obtain a highprecision measurement of the layer thicknesses.
 5. The method of claim 4including producing an interference spectrum by supplementing awavenumber range exceeding the range of photometry with a constantvalue.
 6. The method of claim 4 including calculating the Spatialgramusing a complex power reverse Fourier transformation.